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Search for Dark Neutrino via Vacuum Magnetic Birefringence Experiment
April 4th 2018 Kavli IPMU
Collaborators: X. Fan (Harvard Univ.), S. Kamioka, S. Asai (Tokyo Univ.) experiment
A. Sugamoto (Ochanomizu Univ., OUJ) theory
Kimiko Yamashita (National Tsing Hua University)
PTEP 2017 no. 12, 123B03 (2017), arXiv:1707.03609 (arXiv:1707.03308)
Table of contents1. Introduction 2. Generalized Heisenberg-Euler formula for P
2-1. Effective Action in Proper-time Representation 2-2. Path Integral Representation
3. Effective Lagrangian of Fourth Order 4. Dark Sector Model 5. Relation to the low energy experiment:
Vacuum Magnetic Birefringence Experiment
6. Summary
,
1
Formulation
Phenomenology and Proposal for the Experiment
2
1. Introduction: Vacuum as a “medium”1. Vacuum is a “medium” in which particles and anti-particles are
pair-created and pair-annihilated quantum mechanically
2. We study the magneto-active vacuum in which the constant magnetic field exists as a background
3. We derived a low energy effective Lagrangian including a parity violated term for light-by-light scattering by integrating out the dark fermion and gave constraints on model parameters from a current table-top, low-energy experimental limit Dark Sectors are collections of fields whose couplings with Standard model particles are extremely weak
laser laser
t
1. Introduction: Dark Sector Search
3
SM SM
SM SM
Dark fermion loop
Including Dark Sector as New Physics
Dark fermion: • ψ×1 • P with
t
Including P Interaction
V-A interaction
B0
µ
1. Introduction: QED interaction
4
SM SM
SM SM
electron loop
Parity Conserving Interaction
M. Aaboud et al. [ATLAS Collaboration], ``Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC’’ Nature Phys.13, no. 9, 852 (2017)
t
cf.
1. Introduction: QED CaseW. Heisenberg, H. Euler, Z. Phys. 98, 714 (1936)
Heisenberg-Euler Lagrangian:
from J. Schwinger, Phys. Rev. 82, 664 (1951)
already known
related to this
・・・
Need to Calculate Effective Lagrangian → Vacuum Birefringence Experiment
5
6
Photon Energy
Dark Fermion Mass
Table of contents1. Introduction 2. Generalized Heisenberg-Euler formula for P
2-1. Effective Action in Proper-time Representation 2-2. Path Integral Representation
3. Effective Lagrangian of Fourth Order 4. Dark Matter Model 5. Relation to the low energy experiment:
Vacuum Magnetic Birefringence Experiment
6. Summary
,
7
Formulation
Phenomenology and Proposal for the Experiment
2-1. Effective Action in Proper-time Representation
8
P Action:
Effective Action:
Integrated out
Fµν: Constant → easier to get Leff
Include axial current coupling
Dark fermion: • ψ×1 • P with γ
9
Proper time description:
Quantum mechanics of a point particle with position xµ(s) and spin a(s) at a proper time s
traces of xµ and spin
V. Fock, Physik. Z. Sowjetunion, 12, 404 (1937), Y. Nambu, Prog. Theor. Phys. 5, 82 (1950)
2-1. Effective Action in Proper-time Representation
transition amplitude
x(0) = x(s)
10
If , xµ and spin σµν decouple (this is Heisenberg-Euler case), but they do couple when Parity is violated (our case).
spin
Thisisthedifficultpart
2-2. Path Integral Representation
11The path integration can’t be performed exactly.
= =
Lagrangian is separated into A(s) (free part) and B(s) (interaction part):
Take “tr” for the spin easily, then
A general expression of the effective action can be obtained, even in case of parity violation. However, the contractions by the propagator remain.
12
see J. Schwinger, Phys. Rev. 82, 664 (1951)
gv=-e, gA=0 (g+=0, g-=-e)
reproduce QED result.
= 1 in QED
3. Effective Lagrangian of Fourth Order
13
O(s4) corresponds to O(F4)(sFµν makes no dimension)
extract s4 terms because
dimension 4
14We followed a method developed by SchwingerJ. Schwinger, Phys. Rev.82, 664 (1951)
P
c=0 when gA or gV is 0
3. Effective Lagrangian of Fourth Order
Table of contents1. Introduction 2. Generalized Heisenberg-Euler formula for P
2-1. Effective Action in Proper-time Representation 2-2. Path Integral Representation
3. Effective Lagrangian of Fourth Order 4. Dark Sector Model 5. Relation to the low energy experiment:
Vacuum Magnetic Birefringence Experiment
6. Summary
,
15
Formulation
Phenomenology and Proposal for the Experiment
16
SM + U’(1)Y’ + 1 Complex Scalar
spontaneously broken
4. Dark Sector Model
17
mass diagonalization
Includingthe3rdcomponentofSU(2)Lgaugeboson
We assume
DS DS DS
18
photon in our theory
(massless)
extra U(1) gauge bosonordinary
photon in SM
laser
magnetic field
ψDS
4γ 4γ 4γ, P
19
・OVAL (Observing Vacuum with Laser) experiment
・BMV experiment ・PVLAS experiment
X. Fan etal. Eur. Phys. J. D 71, no. 11, 308 (2017)
Eur. Phys. J. D (2014) 68: 16
Eur. Phys. J. C (2016) 76: 24
laser laser
Input laser
output laser
5. Vacuum Magnetic Birefringence Experiment
Tabletop experiment
mirror
mirror To see QED 1-loop effect (not yet observed)
20
refringence: changing phase velocity of the light birefringence: changing phase velocity of 2 light polarizations in different ways
1 2
medium A
medium B
medium A
medium B
・refractive index: n ・phase velocity: v → n = 1/v
v1
v2v1
v1
x
y
wave propagation
z5. Vacuum Magnetic Birefringence Experiment
21
=D
refractive index: 1/(phase velocity of the laser):
Equation of Motion
5. Vacuum Magnetic Birefringence Experiment
polarization vector ε±
22
To detect birefringence, we observe a difference of polarization state
1) Ellipticity
Polarization Rotation
Elliptically polarized
2) Direction of the long axis of an ellipse
ex) • QED • dark sector in our model
1
2
1
2
ex) dark sector in our model withP
initial polarization
final polarization
initial polarization
final polarization
birefringence birefringence
5. Vacuum Magnetic Birefringence Experiment
23
laser
lineally polarized
Elliptically polarized
laser
Magnetic Field
Output
Input
Ellipticity QED
5. Vacuum Magnetic Birefringence Experiment
24
Conventional: ε(45°)
After a distance L though the magnetic field
ellipticity *
(*) D > 0 in QED
(coefficient of ε(-45°)) / (coefficient of ε(45°))
for QED
5. Vacuum Magnetic Birefringence Experiment
25
To detect P interaction, we propose a new method
P example: ・refractions are occurred for 45 degree or -45 degree polarization modes in different ways ・Polarization with parallel includes both modes. -> We detect perpendicular to see refringence
QED: ・refractions are occurred for parallel (from magnetic field) or perpendicular polarization modes in different ways ・Polarization with 45 degrees includes both modes. -> We detect -45 degrees to see refringence
No QED background
5. Vacuum Magnetic Birefringence Experiment
26
0!After a distance L though the magnetic field with initial state ε||:
5. Vacuum Magnetic Birefringence Experiment
No QED background for the initial state ε||
To detect P interaction, we propose initial state as ε|| -> We detect a perpendicular mode
to see refringence
✏?
D > 0 and Φ=0 in QED
27
Ring Fabry-Perot resonator
Fabry-Perot resonator
mirrormirrormirror
mirror
mirror
mirror
P is reduced if only 2 mirrors
To detect P interaction, we propose a new method
5. Vacuum Magnetic Birefringence Experiment
28
We assume gA = - gV (= |e|) to obtain the experimental constraint ↓ V – A current: Dark neutrino
We examine the case, having both the electron and the lightest DS neutrino. For the DS search, QED forms the background to the DS signal.
DN DNDN+|e|+|e|(1 - γ5)
5. Vacuum Magnetic Birefringence Experiment
29
5. Vacuum Magnetic Birefringence Experiment: Allowed region
J. Jaeckel, Frascati Phys. Ser. 56, 172 (2012)
Log10 [eV]dark photon mass
GeVAt VMB experiment, the sensitivity
does not depend on dark photon mass
We focus on this region
5. Vacuum Magnetic Birefringence Experiment: Conventional, QED/Dark neutrino
30
laser energy: 1 - 4 eV
Experimental LimitExperimental LimitExperimental LimitExperimental Limit
Experimental Limit ⬇︎
QED ~ O(10)!
• QED • dark
neutrino
↑Exclude region
5. Vacuum Magnetic Birefringence Experiment – New Set Up, P DS only
31
allowed
P
Experimental Limit ⬇︎
6. Summary1. We considered Parity violated dark sector model,
and derived generalized Heisenberg-Euler formula 2. Our focus lay on light-by-light scattering effective
Lagrangian of fourth order and gave a result:
3. We focused on Vacuum Magnetic Birefringence Experiment to probe the dark sector and proposed new polarization state and the ring resonator in stead of the usual Fabry-Perot resonator to measure the Parity violated term
32
33
Backup
34
title:SearchforDarkNeutrinoviaVacuumMagneticBirefringenceExperimentabstract:WeconsideradarksectormodelwhereadarkfermioncouplestophotonsviaanextraU(1)mediatorandcancoupletothemediatorwithparityviolation.WederivedalowenergyeffectiveLagrangianincludingaparityviolatedtermforlight-by-lightscatteringbyintegratingoutthedarkfermion.OurfocusliesonVacuumMagneticBirefringenceExperimenttoprobethedarksector.Weproposetheringresonator(3-4mirrors)withanappropriatepolarizationstateoflightinsteadofausualFabry-Perotresonator(2mirrors)withaconventionalpolarizationstateoflighttomeasuretheParityviolatedterm.Weassumethatadarkneutrinoisadarkfermion,i.e.V-Acurrent,andgiveconstraintsonmodelparametersfromacurrentexperimentallimit.PTEP2017no.12,123B03(2017)(arXiv:1707.03308[hep-ph]),arXiv:1707.03609[hep-ph]
35
depends on position, its derivative and appears as non-Gaussian
= =Lagrangian is separated into A(s) (free part) and B(s) (interaction part):
2-2. Path Integral Representation
36
2-2. Path Integral Representation
2. Path integral representation
37
= =
=
Free part
:propagator of A(s)
2. Path integral representation
38
3. Effective Lagrangian of Fourth Order
39
1:
2:
external field
4external fields
5. Vacuum Magnetic Birefringence Experiment
40
described by a,b,c, B(magnetic field), λ(laser beam wave length) , L(beam propagating distance with B)
5. Vacuum Magnetic Birefringence Experiment
41
P
42
2 conditions
t
laserlaser
B B
1 eV
10 Tesla, (1 Tesla ~ 200 eV2)
e
e
e
eΨ with mass m
43
beam energy 1.16 eV @OVAL experiment
Vacuum Magnetic Birefringence Experiment: laser beam energy
For 2 mirrors system: 1 ~ 4 eV laser energy itself: m eV ~ 10 k eV are available thanks to X-ray Free Electron Laser